DEVICE AND METHOD FOR CONTROLLING MOTOR

Abstract: A device and method for controlling an induction motor operated through an inverter at a high speed so that the efficiency of the motor can be always the highest. The device is provided with an effective power measuring means (3) which measures the effective power supplied to a motor (14), a calculating means (1, 2, 4, 5, 6, 7, 8, 16, S₁, S₂, and S₃) which calculate such an AC voltage (V₁) supplied to the motor (14) that the efficiency of the motor (14) becomes the highest, based on the measured effective power and the frequency (f) of the voltage (V₁), and means (9, 10, 11, and 12) which supply the calculated supply voltage (V₁) to the motor (14).

Description: This invention relates to a control unit for motors which is suitable for use in which induction motors (hereafter referred to as "motor") are operated at the maximum efficiency at all times irrespective of load fluctuations (variations). Operation of a motor by inverter is ordinarily carried out under the condition where V (voltage)/f (frequency) is fixed. If operation frequency is determined, the motor experiences slip where the efficiency is maximum. This value takes a fixed value irrespective of whether load is high or low (light or heavy). In the operation where V/f is fixed, if frequency (f) is determined, since voltage (V) is fixed, slip changes when load changes. Accordingly, the efficiency changes, thus failing to achieve out operation at the maximum efficiency at all times. Explanation will now be briefly given by taking examples of conventional technology of this kind. As a method for overcoming lowering of efficiency resulting from change of load which has been proposed as the first conventional example, there is an operation method disclosed in the Tokkohei No. 3-41029 (Japanese Patent Publication No. 41029/1991). This operation method is directed to an operation method for induction motors driven by voltage type inverters, wherein for a time period during which the induction motor is accelerated or decelerated, inverter output voltage is regulated so as to carry out operation by V/f constant control to conduct a control so that ratio V/f between a set inverter output voltage and an inverter output frequency is constant (fixed). In this way, when the induction motor is brought into the mode of constant operation, the method comprises the steps of determining output power P N by performing multiplication of inverter output voltage E DCN and inverter output current i DCN . Decreasing the inverter output voltage from output voltage V 0 at the time of beginning of the constant operation to voltage V 1 dropped (lowered) by ΔV, comparing difference ΔP1 between the inverter output power P 1 calculated at this time and the inverter output power P 0 at the time of beginning of the constant operation with constant ΔP s set in advance, it fixes the inverter output voltage to voltage V 1 if ΔP 1 < ▵P s . On the other hand, further decreasing, the inverter output voltage has elapsed by ΔV from voltage V 1 after a predetermined time if ▵P 1 ≥ ΔP s , a comparison can be made of an output power decrease value at that time and the constant ΔP s , and repeating fixing or further decreasing of the inverter output voltage in dependency upon magnitude of the comparison result to operate the induction motor by inverter output voltage. Further, in the Tokkaihei No. 3-261394 (Japanese Patent Application Laid Open No. 261394/1991) which has been proposed as the second conventional example, there are disclosed a unit and a method adapted for setting, in accordance with load factors, power factors in which power becomes minimum to control voltage so that this power factor is provided. This unit comprises a means for detecting voltage delivered to windings of a motor, means for detecting a current flowing in the winding, power calculation (operation) means connected to the voltage detecting method and the current detecting method, and operative to calculate active (effective) power for at least one cycle from the product of the voltage and the current, and to calculate apparent power for at least one cycle from product of effective value of the voltage and effective value of the current. In addition, the method for setting optimum power factor command value of the motor; the comparison means for calculating measurement power factor from the active power and the apparent power to compare the measurement power factor and the set power factor to generate a power factor comparison signal; and voltage regulation method responsive to the power factor comparison signal to regulate voltage delivered to the windings of the motor, wherein the means regulates the voltage so as to allow the measurement power factor to become close to the optimum power factor. Further, the above-mentioned method is a control method comprising steps for performing the previously described respective means. However, in the method of the first conventional example, there is the problem that since it takes considerable time until power arrives at the minimum point because the minimum operation state of power is searched while carrying out very small change of voltage, response with respect to load change is poor. Moreover, in the method of the second conventional example, there is included the problem that while operation can be performed so that power becomes minimum, since voltage at which power becomes minimum and voltage at which efficiency becomes maximum are generally different as indicated by Fig. 1 which will be described later, the operation at the voltage where power becomes minimum would be operation at a portion shifted from the maximum efficiency (slip). US-A-4 207 510 discloses a method and apparatus for operation of a brushless d.c. motor, by using a controller responsive to motor input current and voltage. The difference between first and second impedance related signals is used to control the motor input voltage for efficient motor operation over a wide range of operating speeds. FR-A-2 577 730 discloses a further apparatus for reducing the energy consumed by an electric motor. This apparatus, too, uses a controller which monitors voltage supplied to the motor and adjusts motor current supply accordingly. JP-A-53 16793 discloses a control unit for a motor which comprises supply voltage calculation means. This invention is a means which has been carried out in view of respective problems as described above, and is directed to a unit aiming at conducting control at a high speed so that efficiency of the motor is maximum at all times with respect to load changes. This invention is directed to a control unit for a motor which is adapted for controlling motor operation by an inverter as set out in claims 1 to 5. Since this invention is directed to such motor control units, optimum voltage can be delivered to the motor depending on load conditions. Accordingly, it is possible to operate the motor at the maximum efficiency while always and quickly conforming to load conditions, etc. Fig. 1 is a view showing input power versus efficiency of the motor when input voltage of the motor is changed under the condition where motor load is fixed, Fig. 2 is a T-type equivalent circuit diagram of the motor, Fig. 3 is a view showing the case where the value of coefficient K 1 when frequency as contained in this invention is rigorously calculated and the case where that value is calculated so as to become proportional to the cube root of frequency. Fig. 4 is a block diagram showing a circuit configuration in the characteristics of this invention. This utilization will now be described with reference to the attached drawings. Fig. 1 is a view showing the relationship between input power and efficiency of the motor when input voltage of the motor is changed under the condition where load of the motor is fixed. This is a characteristic curve when input power (first ordinate) and efficiency (second ordinate), which correspond to input voltage (abscissa) at the rated voltage of 200 V and rated power of 2.2 KW and load factor 10% of the motor are plotted on the same plane, wherein point 102 where input power becomes minimum is an input voltage clearly different from point 101 where efficiency becomes maximum. A T-type equivalent circuit of the motor of a utilization of this invention is shown in Fig. 2. In Fig. 2, V 1 denotes phase voltage; r 1 denotes primary resistance; x 1 denotes leakage reactance; I 1 denotes primary current; E 1 denotes primary voltage; r 2 denotes secondary resistance converted into the primary side; x 2 denotes secondary leakage reactance converted into the primary side; I 2 denotes secondary current converted into the primary side; s denotes slip; r m denotes iron loss resistance; x m denotes excitation reactance; and I M denotes excitation current. When g m is excitation conductance, b m is excitation susceptance and j is complex number symbol. The following equation derives from the above-mentioned equivalent circuit. Vector I M = (vector E 1 )/(r m + jx m ) = (vector E 1 ) × (g m - jb m ) In the above equation, g m = r m /(r m 2 + x m 2 ) b m = x m /(r m 2 + x m 2 ) Vector I 2 = (vector E 1 )/{(r 2 /s) + jx 2 } = (vector E 1 ) × [{sr 2 /(r 2 2 + s 2 x 2 2 )} -j{s 2 x 2 /(r 2 2 + s 2 x 2 2 )}] = (vector E 1 ) × (a 1 - ja 2 ) In the above equation, a 1 = sr 2 /(r 2 2 + s 2 x 2 2 ) a 2 = s 2 x 2 /(r 2 2 + s 2 x 2 2 ) Vector I 1 = (vector I M ) + (vector I 2 ) = (vector E 1 ) × {(a 1 + g m )-j(a 2 + b m )} = (vector E 1 ) × (b 1 - jb 2 ) In the above equation, b 1 = a 1 + g m b 2 = a 2 + b m Vector V 1 = (vector E 1 ) + (r 1 + jx 1 ) × (vector I 1 ) = (vector E 1 ) × {(1 + b 1 r 1 + b 2 x 1 ) -j(b 2 r 1 - b 1 x 1 )} = (vector E 1 ) × (c 1 - jc 1 ) In the above equation, c 1 = + b 1 r 1 + b 2 x 1 c 2 = b 2 r 1 - b 1 x 1 From the equations (3), (4), Vector I 1 = {(b 1 - jb 2 )/(c 1 - jc 2 )}V 1 Apparent power P 1e delivered to the motor is expressed as follows. P 1e = 3 x (vector V 1 ) × (conjugate vector of I 1 ) = {3(b 1 + jb 2 )/(c 1 + jc 2 )}V 1 2 = {3V 1 2 /(c 1 2 + c 2 2 )} × {(b 1 c 1 + b 2 c 2 ) -j(b 1 c 2 - b 2 c 1 )} Since effective power P 1 of the primary input of the motor is given by the real part of the equation (6), P 1 = {3(b 1 c 1 + b 2 c 2 )/c 1 2 + c 2 2 )}V 1 2 Apparent power P 2e of the secondary input of the motor is expressed as follows. P 2e = 3 × (vector E 1 ) × (conjugate vector of I 2 ) = 3 × (vector E 1 ) × (conjugate vector of E 1 ) × (a 1 + ja 2 ) = {3V 1 2 /(c 1 2 + c 2 2 )} × (a 1 + ja 2 ) Since effective power P2 of the secondary input of the motor is given by the real part of the equation (8), P 2 = 3V 1 2 a 1 /(c 1 2 + c 2 2 ) Since mechanical output P 2m is the value obtained by multiplying effective power P 2 of the secondary input by (1-s), P 2m = {3a 1 (1-s)/(c 1 2 + c 2 2 } x V 1 2 Efficiency η of the motor is expressed as follows. η = P 2m /P 1 = (1-s)a 1 /(b 1 c 1 + b 2 c 2 ) Since a 1 , b 1 , b 2 , c 1 , c 2 are parameters (variables) (varying) as a function of motor constant, frequency and slip s in the above equation, efficiency η also becomes a parameter (variable) as a similar function. Slip s which provides the maximum efficiency is obtained by determining slip s where the equation obtained by differentiating the equation (11) by s is equal to zero. Assuming now that slip at this time is s (η max ) , since slip s (η max ) which provides the maximum efficiency varies as a function of constant and frequency of the motor, the slip s (η max ) becomes equal to constant value irrespective of load. On the other hand, effective power P 1 of the primary input of the motor is expressed as below from the equation (7): P 1 = {3(b 1 c 1 + b 2 c 2 )/(c 1 2 + c 2 2 )} × V 1 2 When line voltage V L is substituted for phase voltage of V 1 , V L = V 1 /(3) 1/2 Subtitution of line voltage V L into the equation (7) gives: P 1 = {(b 1 c 1 + b 2 c 2 )/(c 1 2 + c 2 2 )} × V L 2 When line voltage V L is determined from the above equation, V L = {(c 1 2 + c 2 2 )/(b 1 c 1 + b 2 c 2 )} 1/2 × P 1 1/2 = K 1 P 1 1/2 In the above equation, K 1 = {(c 1 2 + c 2 2 )/(b 1 c 1 + b 2 c 2 )} 1/2 Since b 1 , b 2 , c 1 , c 2 are are parameters varying as a function of motor constant, frequency, slips, and coefficient K 1 also become parameters varying as a similar function. If load changes, slip s changes. Accordingly, coefficient K 1 also changes. However, when an approach is employed to control line voltage V L so that slip s becomes equal to slip s (η max ) which provides the maximum efficiency at all times irrespective of load change, value of coefficient K 1 also becomes equal to a fixed value irrespective of load changes. In other words, if the product of coefficient K 1 at the time of slip s (η max ) which provides the maximum efficiency and the square root of detected effective power P 1 of the primary input of the motor is given as input voltage of the motor, slip maintains s (η max ) . Accordingly, it is possible to operate the motor at the maximum efficient at all times with respect to load changes. However, since the equation obtained by differentiating the equation (11) by slip s is put so that it is equal to zero is equation of the sixth degree. Since this equation cannot be analytically solved, coefficient K 1 is determined by approximation as described below. When the equations (3a), (3b), (4a), (4b) are applied to the equation (11), efficiency η is expressed as follows. η = {(1-s)a 1 } / (g m + g m r 1 b 1 + g m x 1 b 2 + a 1 + r 1 a 1 b 1 + x 1 a 1 b 2 + r 1 b m b 2 + r 1 a 2 b 2 - x 1 b m b 1 - x 1 a 2 b 1 ) Since, in the equation (13), (g m x 1 b 2 ), (r 1 a 2 b 2 ), (x 1 a 2 b 1 ) are small as compared to other terms and (x 1 a 1 b 2 ) ≒ (x 1 b m b 1 ), they are disregarded. Thus, the equation (13) is expressed as follows. η = {(1-s)a 1 } /(g m + a 1 + r 1 a 1 b 1 + r 1 b m b 2 + g m r 1 b 1 ) Moreover, since r 2 2 >> s 2 x 2 2 in the equations (2a), (2b), s 2 x 2 2 of respective denominator of the equations are disregard, the following equations are provided. a 1 ≒ s/r 2 a 2 ≒ (x 2 s 2 )/r 2 2 In addition, from the equations (3a), (3b), b 1 ≒ g m + s/r 2 b 2 ≒ b m + x 2 (s 2 /r 2 2 ) Subtitution of these equations into the equation (14) gives: η = {(1-s)sr 2 } / {r 1 s 2 + r 2 (2r 1 g m + 1)s + r 2 2 (g m + r 1 b m 2 )} Substituting dη/ds=0 to determine slip s. Thus, slip s (η max ) which provides the maximum efficiency is determined. Substituting A = {r 2 (2r 1 g m + 1)}/r 1 B = {r 2 2 (g m + r 1 b m 2 )} /r 1 slip s (η max ) which provides the maximum efficiency is expressed as follows. s (η max ) = [ -B + {B x (A+B+1)} 1/2 ]/(A + 1) Since A, B are parameters varying as a function of motor constant and frequency, s (η max ) which provides the maximum efficiency is also a parameter varying as a function of similar function. When the equations (4a), (4b) are applied in the equation (12a), c 1 2 + c 2 2 = 1 + r 1 2 b 1 2 + x 1 2 b 2 2 + 2r 1 b 1 + 2x 1 b 2 + r 1 2 b 2 2 + x 1 2 b 1 2 Since (r 1 2 b 2 2 ), (x 1 2 b 2 2 ) are small to such a degree that they can be disregarded as compared to other terms, c 1 2 + c 2 2 ≒ 1 + r 1 2 b 1 2 + 2r 1 b 1 + 2x 1 b 2 + x 1 2 b 1 2 When the equations (3a), (3b) are applied to the above equation, c 1 2 + c 2 2 ≒ r 1 2 g m + 2a 1 r 1 2 g m + r 1 2 a 1 2 + r 1 2 b m 2 + 2r 1 2 a 2 b m +r 1 2 a 2 2 + 2r 1 g m + 2r 1 a 1 + 2x 1 b m + 2x 1 a 2 + 1 since (r 1 2 g m ), (2r 1 2 a 2 b m ), (r 1 2 a 2 2 ), (2x 1 a 2 ) are small as compred to other terms, they are disregarded. Thus, the following expression is obtained. c 1 2 + c 2 2 ≒ 2a 1 r 1 2 g m + r 1 2 a 1 2 + r 1 2 b m 2 + 2r 1 g m + 2r 1 a 1 + 2x 1 b m + 1 Substitution of a 1 ≒ η s/r 2 of the equation (14a) and a 2 ≒ (x 2 s 2 )/r 2 2 of the equation (14b) into the above equation gives: c 1 2 + c 2 2 ≒ (1/r 2 2 ) × (2r 1 2 r 2 g m s + r 1 2 s 2 + r 1 2 r 2 2 b m 2 + 2r 1 r 2 2 g m + 2r 1 r 2 s + 2x 1 r 2 2 b m + r 2 2 ) Similarly, b 1 c 1 + b 2 c 2 ≒ (1/r 2 2 ) × (r 2 2 g m + 2r 1 r 2 g m s + r 2 s + r 1 s 2 + r 1 r 2 2 b m 2 ) Substitution of these (c 1 2 + c 2 2 ) and (b 1 c 1 + b 2 c 2 ) into the equation (12a) is made, and coefficient K 1 when slip s is caused to be s (η max ) , is expressed as follows. K 1 = [{r 1 2 (s (η max ) ) + 2r 1 r 2 (r 1 g m + 1) x s (η max ) + r 2 2 (r 1 2 b m 2 + 1) + 2r 2 2 (r 1 g m + x 1 b m }/ {r 1 (s (η max ) )2 + r 2 (2r 1 g m + 1) x s (η max ) + r 2 2 (g m + r 1 b m 2 }] 1/2 This equation (17) provides a good approximated value in a broad range of the motor capacity and the operation frequency. When the product of coefficient K 1 calculated by the equation (17) and the square root of detected primary input power P 1 of the motor is given as an input voltage, it is possible to operate the motor at the maximum efficiency. In order to operate the motor at the maximum efficiency, as previously described, there is required a calculation means for determining s (η max ) capable of operating the motor at the maximum efficiency by the equation (16) to apply such slip value to the equation (17) thus to determine value of coefficient K 1 . If calculation is carried out by this procedure, it is possible to calculate, with good accuracy, voltage which provides the maximum efficiency, delivered to the motor. However, since the quantity of calculations is great, if attempt is made to realize high speed response, the unit becomes expensive. In accordance with the numeric calculation, value of coefficient K 1 indicated by the equation (17) is substantially proportional 1 to the cubic-root of frequency. When value of coefficient K 1 when frequency f is changed in the equation (17) is examined, result is as shown in Fig. 3. While three types of motors of 1.5 KW, 7.5 KW, and 55 KW are shown in the example of Fig. 3, motors of other capacities show a substantially similar tendency. Solid lines of Fig. 3 indicate results obtained by plotting values of coefficient K 1 at respective frequencies determined by using an approximate calculation method of Newton on the basis of the equation (11), and broken lines are the results obtained by determining values of coefficient K 1 at the time of 60 Hz by the approximate calculation method of Newton to allow this value to be coefficient K 60 to determine values of coefficient K 1f at the operation frequency f by the following equation to plot them. K 1f = {K 60 /(60) 1/3 } (f) 1/3 = K 2 (f) 1/3 In the above equation, K 2 = K 60 /(60) 1/3 It is seen that the value coefficient K 1 is substantially proportional to the cubic square of frequency. It is not necessary that the fundamental frequency is 60 Hz. Generally, an approach may be employed in which the fundamental frequency is caused to be f 0 to determine, with good accuracy, value K f0 of coefficient K 1 when the fundamental frequency is f 0 to determined the value of coefficient K 1f at the operation frequency f on the basis of value K f0 as follows. K 1f = {K f0 /(f 0 ) 1/3 }(f) 1/3 When the value of coefficient K 1 when operation frequency is changed is determined by the equation (18) or (19), calculation time is shortened, thus making it possible to improve response. When consideration is collectively made, line voltage V L of supply voltage to the motor which provides the maximum efficiency, V L = K 1 · (P 1 ) 1/2 = K f0 · (f/f 0 ) 1/3 · (P 1 ) 1/2 Supply voltage to the motor is calculated by the equation (20) by effective power of the motor and is delivered to the motor. However, if filter time constant for detection of power is small, there is a lack of stability lacks, while if such filter constant is prolonged, response becomes poor. To solve this problem, two time constants are used [of course three time constants or more may be used and fine control is conducted depending upon the circumstances] to use a filter of short time constant when change of power is great; to use a filter of long time constant when that change is small; and to fix detected power when change of power is even smaller to deliver a fixed voltage to the motor, thus to achieve more stabilization. A block diagram of the circuit configuration contained in this invention is shown in Fig. 4, and the explanation will now be given. In Fig. 4, reference number 1 is a soft starter for avoiding sudden rising (increase) of speed at the time of starting of the motor to gently start operation. Reference number 2 is a frequency-to-voltage converter; reference number 3 is a power detector; reference number 4 denotes a filter of time constant T 1 ; reference number 5 is a filter of time constant T 2 [T 1 < T 2 ] reference number 6 is a frequency f-to-coefficient K 1 converter; reference number 7 is a calculator (operation element) for introducing detected power P and coefficient K 1 to multiply the square root of power P by coefficient K 1 to calculate line voltage (supply voltage) V L ; reference number 8 is a limiter in which line voltage V L is taken on the abscissa and command voltage V 0 is taken on the ordinate; reference number 9 is a driver; reference number 10 denotes an inverter; reference number 11 is a commercial A.C. power supply; reference number 12 is a converter; reference number 13 is a smoothing circuit; reference number 14 is a motor to be driven; reference number 15 is a motor operation frequency command element; reference number 16 is a memory circuit for storing detected power at the last sampling period in detection of power, and S 1 ∼ S 3 are changeover (selector) switches. It is now assumed that changeover switch S 1 is initially in "open" state. Operation frequency f from the frequency command element 15 is passed through soft starter 1, wherein it increases from frequency zero toward f by a set time gradient. The frequency-to-voltage converter 2 is a unit adapted for generating voltage corresponding to frequency outputted from the soft starter 1, and serves to conduct a control so that the ratio between voltage and frequency delivered to the motor is fixed. At the time of starting of the motor, the motor is operated by the above-mentioned operation. When output of the soft starter 1 reaches the command frequency f, the changeover switch S 1 is switched to "closed" . At subsequent times, operation is continued by the control method of this invention. Effective power delivered to motor 14 is detected from voltage [V 1 ] and current [I 1 ] is delivered to motor 14 by the power detector 3. This effective power is introduced to the two filters 4 and 5. Filter 4 has short time constant T 1 , and filter 5 has long time constant T 2 . Moreover, changeover switches S 2 , S 3 are in "open" state in the beginning. When change of power is less than set value ΔP 1 , the changeover switch S 2 is brought into closed state. Thus, filter 5 of long time constant is used for detecting effective power. When change of power further becomes smaller and becomes less than value ΔP 2 (ΔP 2 < ΔP 1 ), the changeover switch S 3 is brought into "closed" state. Thus, power is fixed to that at the time point when change of power is below ΔP 2 as detected power P 1 , and that power is stored into memory circuit 16. The power thus stored continues to be outputted. The frequency f-to-coefficient K 1 converter 6 calculates constant (coefficient) K 1 with respect to frequency command f. Calculator 7 calculates, from coefficient K 1 calculated at converter 6 and detected power P 1 , a voltage where efficiency of motor 14 becomes maximum. Limiter 8 is provided for prevention of over-excitation or prevention of stalling when speed is too low. The voltage Vo and the frequency command f which have been calculated in this way are delivered to driver 9. Thus, driver 9 controls transistors of inverter 10 so that line voltage V L and frequency command f are delivered to motor 14. As stated above, since the motor is driven by supply (line) voltage corresponding to effective power/frequency command of the motor constantly in this circumstance, the motor is quickly operated at the maximum efficiency at all times as explained in detail in the above-mentioned framing of theory. As is clear from the foregoing description, in accordance with this invention, there is provided the excellent advantage that optimum voltage is delivered at a high speed to the motor in correspondence with load state so that the motor can be operated at the maximum efficiency at all times.

Claims: A control unit for a motor, which is adapted for controlling motor operation by an inverter, the unit comprising: a means (3) for detecting effective power delivered to the motor; a calculation means (6,7,8) for calculating, as a supply voltage which provides the maximum efficiency, the product of coefficient K1 determined by calculation from a constant, a value derived from the supply frequency of the motor and the square root of the detected effective power of the motor; and a means (9) for delivering the calculated supply voltage to the motor. A control unit for a motor, which is adapted for controlling motor operation by an inverter, the unit comprising: a means (3) for detecting effective power delivered to the motor; a calculation means (6,7,8) for calculating,; as a supply voltage which provides the maximum efficiency, the product of coefficient K2 determined by calculation from a constant, a value (f/f 0 ) 1/3 , where f is supply frequency and f 0 a specific frequency, and the square root of the detected effective power of the motor and; a means (9) for delivering the calculated supply voltage to the motor. A control unit for a motor as set forth in claim 1 or 2, wherein the effective power detecting means (3) is operative so that in the case where change of effective power is assumed to be a first constant ▵ P 1 , it detects effective power by using a power detection filter of a larger time constant. A control unit for a motor as set forth in claim 3, wherein the effective power detecting means (3) is operative so that in the case where change of effective power is assumed to be a second constant Δ P 2 which is smaller than said first constant Δ P 1 , it fixes the detected power P1 at the time when the change of detected power became said second constant Δ P2, as a detection value of effective power, while when change of effective power continues to be less than Δ P 2 , it allows the fixed power to be a detected effective power. A control unit for a motor as set forth in claim 1, wherein the coefficient K 1 is expressed as K 1 =[{r 1 2 (S (η max ) ) 2 +2r 1 r 2 (r 1 g m +1) × S (η max ) +r 2 2 (r 1 2 b m 2 +1) +2r 2 2 (r 1 g m +x 1 b m )}/{r 1 (S (η max ) ) 2 +r 2 -(2r 1 g m +1)×S (η max ) +r 2 2 (g m +r 1 b m 2 )}] 1/2 where r 1 is motor primary resistance, x, is primary leakage reactance of motor, S (η max ) is slip of motor where efficiency of the motor is maximum, r 2 is secondary resistance converted into the primary side of motor, b m is excitation susceptance of the motor, and g g is excitation conductance of the motor.

Inventors: YAMAKAWA TAKAYUKI, YAMAKAWA, TAKAYUKI, YAMAKAWA, TAKAYUKI KABUSHIKI-KAISHA YASKAWA DENKI
Applicants: YASKAWA DENKI SEISAKUSHO KK, KABUSHIKI KAISHA YASKAWA DENKI
Application year: 1994
Main classification: H02P7
IPC codes: H02P27, H02P23, H02M7